My max snatch is a measly 190lb using a grip that leaves my pointer on the smooth part of the bar. At times I notice that I pull early (bar hits the thighs as if I am cleaning) but I am fast enough to get under and that width makes me strong enough to catch and stabilize.

My coach says I should widen my grip to about slightly less than a thumbs length from the smooth part but I have a more difficult time pulling it and getting under. I struggle greatly holding 165 from a wider grip.

I'm simply not sure if I should just keep the initial grip length and just focus on delaying the pull, or if I should go wider and just improve from there.

I'm assuming by "smooth part" you mean the ring that in the middle of the nurling and not the smooth part in the middle.

If your more stable overhead with your current grip then just be more patient with the pull. If you're being as patient as you can be and your still hitting the thighs then I would move the grip out. There are ways you can strengthen the overhead position in the Snatch.